Space of modular forms of level 49, weight 5, and Character 49.d

• Label: 49.5.d
• Level: $49$
• Weight: $5$
• Character orbit: 49.d
• Rep. character: $\chi_{49}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $22$
• Newform subspaces: $3$
• Sturm bound: $23$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	49.d (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(23\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(49, [\chi])\).

	Total	New	Old
Modular forms	46	30	16
Cusp forms	30	22	8
Eisenstein series	16	8	8

Trace form

22 * q + 7 * q^2 - 6 * q^3 - 57 * q^4 + 30 * q^5 - 502 * q^8 + 247 * q^9 + 204 * q^10 + 28 * q^11 + 588 * q^12 - 796 * q^15 + 19 * q^16 + 246 * q^17 - 205 * q^18 - 642 * q^19 + 2228 * q^22 - 728 * q^23 - 720 * q^24 + 995 * q^25 - 1008 * q^26 + 2788 * q^29 - 528 * q^30 - 3618 * q^31 - 2277 * q^32 - 2070 * q^33 + 5818 * q^36 - 1344 * q^37 + 6168 * q^38 + 6244 * q^39 + 1752 * q^40 - 15300 * q^43 - 942 * q^44 - 1944 * q^45 - 4090 * q^46 + 1542 * q^47 - 2294 * q^50 + 7242 * q^51 + 3192 * q^52 - 4424 * q^53 + 11016 * q^54 - 7348 * q^57 + 15358 * q^58 - 2526 * q^59 - 3612 * q^60 + 282 * q^61 - 2790 * q^64 - 24444 * q^65 + 2556 * q^66 + 1176 * q^67 - 20412 * q^68 + 15388 * q^71 + 2723 * q^72 - 5214 * q^73 + 6410 * q^74 + 9636 * q^75 + 35840 * q^78 + 9632 * q^79 + 3144 * q^80 - 687 * q^81 + 4032 * q^82 + 8332 * q^85 - 31234 * q^86 - 5976 * q^87 + 35166 * q^88 - 33990 * q^89 - 62676 * q^92 - 2138 * q^93 - 27768 * q^94 - 15930 * q^95 + 37284 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(49, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
49.5.d.a	$49$	$5$	49.d	7.d	$6$	$2$	$1$	$5.065$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-7}) \)					7.5.b.a	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q-\zeta_{6}q^{2}+(15-15\zeta_{6})q^{4}-31q^{8}+\cdots\)
49.5.d.b	$49$	$5$	49.d	7.d	$6$	$4$	$2$	$5.065$	\(\Q(\sqrt{-3}, \sqrt{22})\)	None					7.5.d.a	$2$	$0$	\(-4\)	\(-6\)	\(30\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\beta _{1}-2\beta _{2})q^{2}+(-2+\beta _{1}+\cdots)q^{3}+\cdots\)
49.5.d.c	$49$	$5$	49.d	7.d	$6$	$16$	$8$	$5.065$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		49.5.b.b	$4$	$0$	\(12\)	\(0\)	\(0\)	\(0\)	$7^{12}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\beta _{2}+\beta _{12})q^{2}+\beta _{5}q^{3}+(5\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(49, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(49, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)